Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s w...

In this paper we establish the existence and uniqueness of a coupled fixed point for operators F : X ×X → X satisfying a new type of contractive condition, which is weaker than all the corresponding ones studied in literature so far. We also provide constructive features to our coupled fixed point results by proving that the unique coupled fixed point of F can be approximated by means of two di...

A new nonlinear iterative method for nonlinear parabolic equation is developed and applied to a multimaterial nonequilibrium radiation diffusion problem on distorted meshes. The new iterative method is named by Picard-Newton method (PN for short). Solution process of the method is as follows. First, by linearizing the time-discretized nonlinear partial differential equation(PDE), we can get an ...

Orders on surfaces provided a rich source of examples of noncommutative surfaces. In [HS05] the authors prove the existence of the analogue of the Picard scheme for orders and in [CK11] the Picard scheme is explicitly computed for an order on P ramified on a smooth quartic. In this paper, we continue this line of work, by studying the Picard and Hilbert schemes for an order on P ramified on a u...

Orders on surfaces provided a rich source of examples of noncommutative surfaces. In [HS05] the authors prove the existence of the analogue of the Picard scheme for orders and in [CK11] the Picard scheme is explicitly computed for an order on P ramified on a smooth quartic. In this paper, we continue this line of work, by studying the Picard and Hilbert schemes for an order on P ramified on a u...

This paper investigates a polygonal finite element (PFE) to solve two-dimensional (2D) incompressible steady fluid problem in cavity square. It is well-known standard benchmark (i.e., lid-driven flow)-to evaluate the numerical methods solving problems controlled by Navier–Stokes (N–S) equation system. The approximation solutions provided this research are based on our developed equal-order mixe...

We introduce a new family of numerical algorithms for approximating solutions general high-dimensional semilinear parabolic partial differential equations at single space-time points. The algorithm is obtained through delicate combination the Feynman-Kac and Bismut-Elworthy-Li formulas, an approximate decomposition Picard fixed-point iteration with multilevel accuracy. has been tested on variet...

The inverse reflector problem arises in geometrical nonimaging optics: Given a light source and a target, the question is how to design a reflecting free-form surface such that a desired light density distribution is generated on the target, e.g., a projected image on a screen. This optical problem can mathematically be understood as a problem of optimal transport and equivalently be expressed ...